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I am unable to understand how to solve this question, please send the working out.

I am unable to understand how to solve this question, please send the working out-example-1
User Asura
by
4.5k points

2 Answers

3 votes
1 Move the negative sign to the left.
(
9
x
)
1
2
8
x

1
2
3
(9x)

​2

​1
​​
​​
​3
​​ √
​8x
​−
​2

​1
​​
​​

​​

2 Convert
(
9
x
)
1
2
(9x)

​2

​1
​​
​​ to square root.
9
x
8
x

1
2
3

​9x

​​
​3
​​ √
​8x
​−
​2

​1
​​
​​

​​

3 Use this rule:
a
b
=
a
b

​ab

​​ =√
​a

​​ √
​b

​​ .
9
x
8
x

1
2
3

​9

​​ √
​x

​​
​3
​​ √
​8x
​−
​2

​1
​​
​​

​​

4 Since
3
×
3
=
9
3×3=9, the square root of
9
9 is
3
3.
3
x
8
x

1
2
3
3√
​x

​​
​3
​​ √
​8x
​−
​2

​1
​​
​​

​​

5 Use Multiplication Distributive Property:
(
x
y
)
a
=
x
a
y
a
(xy)
​a
​​ =x
​a
​​ y
​a
​​ .
3
x
8
3
x

1
2
3
3√
​x

​​
​3
​​ √
​8

​​
​3
​​ √
​x
​−
​2

​1
​​
​​

​​

6 Calculate.
3
x
×
2
x

1
2
3
3√
​x

​​ ×2
​3
​​ √
​x
​−
​2

​1
​​
​​

​​

7 Use this rule:
(
x
a
)
b
=
x
a
b
(x
​a
​​ )
​b
​​ =x
​ab
​​ .
3
x
×
2
x

1
2
×
3
3√
​x

​​ ×2x

​2×3

​−1
​​
​​

8 Simplify
2
×
3
2×3 to
6
6.
3
x
×
2
x

1
6
3√
​x

​​ ×2x

​6

​−1
​​
​​

9 Move the negative sign to the left.
3
x
×
2
x

1
6
3√
​x

​​ ×2x
​−
​6

​1
​​
​​

10 Use Negative Power Rule:
x

a
=
1
x
a
x
​−a
​​ =
​x
​a
​​

​1
​​ .
3
x
×
2
×
1
x
6
3√
​x

​​ ×2×

​6
​​ √
​x

​​

​1
​​

11 Use Quotient Rule:
x
a
x
b
=
x
a

b
​x
​b
​​

​x
​a
​​
​​ =x
​a−b
​​ .
\[3\times 2\sqrt[2}-\frac{1}{6]{x}\]

12 Simplify
1
2

1
6
​2

​1
​​ −
​6

​1
​​ to
1
3
​3

​1
​​ .
3
×
2
x
3
3×2
​3
​​ √
​x

​​

13 Simplify.
6
x
3
6
​3
​​ √
​x

​​
User Sid Sarasvati
by
4.9k points
2 votes

Answer:


(9x)^{(1)/(2) }.(8x^{(-1)/(2) })^{(1)/(3) }\\\\=9^(1/2).x^(1/2).8^(1/3).x^(-1/2.1/3) \\\\=3.2.x^(1/2).x^(-1/6) \\\\\\=6.x^(1/2-1/6)\\\\=6x^(1/3)

Explanation:

User Sathyajith Bhat
by
4.8k points